In this book Terence Parsons revives the older tradition of taking such objects at face value. Using various modern techniques from logic and the philosophy of language, he formulates a metaphysical theory of nonexistent objects. The theory is given a formalization in symbolism rich enough to contain definite descriptions, modal operators, and epistemic contexts, and the book includes a discussion which relates the formalized theory explicitly to English.

Anthony Everett gives a philosophical defence of the common-sense view that there are no such things as fictional people, places, and things. He argues that our talk and thought about such fictional objects takes place within the scope of a pretense, and that we gain little but lose much by accepting fictional realism.

Contingent negative existentials give rise to a notorious paradox. I formulate a version in terms of metaphysical grounding: nonexistence can't be fundamental, but nothing can ground it. I then argue for a new kind of solution, expanding on work by Kit Fine. The key idea is that negative existentials are contingently zero-grounded – that is to say, they are grounded, but not by anything, and only in the right conditions. If this is correct, it follows that grounding cannot be (...) an internal relation, and that no complete account of reality can be purely fundamental. (shrink)

This paper argues for a distinction between fictional characters, as parts of intentionally created abstract artifacts, and intentional objects, as nonexistent objects generated by referential acts that fail to refer. It argues that intentional objects as the nonexistent objects of imagination and other objectual attitudes are well-reflected in natural language, though in a highly restricted way, reflecting their ontological dependence on referential acts. The paper elaborates how that ontological dependence can be understood.

Are there nonexistent objects, i.e., objects that do not exist? Some examples often cited are: Zeus, Pegasus, Sherlock Holmes, Vulcan (the hypothetical planet postulated by the 19th century astronomer Le Verrier), the perpetual motion machine, the golden mountain, the fountain of youth, the round square, etc. Some important philosophers have thought that the very concept of a nonexistent object is contradictory (Hume) or logically ill-formed (Kant, Frege), while others (Leibniz, Meinong, the Russell of Principles of Mathematics) have embraced it wholeheartedly. (...) This entry is an examination of the many questions which arise in connection with the view that there are nonexistent objects. The following are particularly salient: What reasons are there (if any) for thinking that there are nonexistent objects? If there are nonexistent objects, then what kind of objects are they? How can they be characterized? Is it possible to provide a consistent theory of nonexistent objects? What is the explanatory force of a consistent theory of nonexistent objects (if such a thing is possible)? (shrink)

A nonexistent possible is a particular concrete object which exists in some possible world but doesn't exist in the actual world. A definite description may be said to individuate a nonexistent possible if just one possible object satisfies the condition specified by that description, and this possible object doesn't exist in the actual world. Given a plausible form of mereological essentialism, certain mereological and causal descriptions which determine a thing's composition individuate nonexistent possible hunks of matter which are mereological or (...) causal products of actual objects. Other sorts of descriptions such as 'the possible fat man in that doorway' and ones associated with typical fictional, imaginary, and mythical things do not individuate a nonexistent possible, and it is problematical whether we can individuate a nonexistent possible which is disjoint, viz., one which is not a mereological or causal product of actual objects. (shrink)

A nonexistent possible is a particular concrete object which exists in some possible world but doesn't exist in the actual world. A definite description may be said to individuate a nonexistent possible if just one possible object satisfies the condition specified by that description, and this possible object doesn't exist in the actual world. Given a plausible form of mereological essentialism, certain mereological and causal descriptions which determine a thing's composition individuate nonexistent possible hunks of matter which are mereological or (...) causal products of actual objects. Other sorts of descriptions such as 'the possible fat man in that doorway' and ones associated with typical fictional, imaginary, and mythical things do not individuate a nonexistent possible, and it is problematical whether we can individuate a nonexistent possible which is disjoint, viz., one which is not a mereological or causal product of actual objects. (shrink)

Serious actualism is the view that it is metaphysically impossible for an entity to have a property, or stand in a relation, and not exist. Fine (1985) and Pollock (1985) influentially argue that this view is false. In short, there are properties like the property of nonexistence, and it is metaphysically possible that some entity both exemplifies such a property and does not exist. I argue that such arguments are indeed successful against the standard formulation of serious actualism. However, (...) I also argue that we should distinguish a weaker formulation of serious actualism using the actualist distinction between truth in, and truth at, a possible world. This weaker formulation is then shown to be consistent with the existence and possible exemplification of properties like the property of nonexistence. I end with a novel argument for the truth of the weaker formulation. (shrink)

According to Meinongianism, some objects do not exist but we can legitimately refer to and quantify over them. Moreover, Meinongianism standardly regards nonexistent objects as contributing to the truth-makers of sentences about nonexistent objects. Recently, Tim Crane has proposed a weak form of Meinongianism, a reductionism, which denies any contribution of nonexistent objects to truth-making. His reductionism claims that, even though we can truly talk about nonexistent objects by using singular terms and quantifiers about them, any truth about nonexistent objects (...) is reducible to some truths about existent objects. In this paper, we critically examine the reductionism casting some doubts on the reducibility of truths of sentences like ‘a winged pig is possible’ or ‘some winged pig does not exist’ into truths about existent objects. We also argue that the truth of such sentences can be explained by adopting a strong form of Meinongianism which admits contribution of nonexistent objects to the truth-making of such sentences. (shrink)

Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove--again in ZFC--that for a large class of cardinals there is no universal linear order (e.g. in every regular $\aleph_1 < (...) \lambda < 2^{\aleph_0}$). In fact, what we show is that if there is a universal linear order at a regular λ and its existence is not a result of a trivial cardinal arithmetical reason, then λ "resembles" ℵ1--a cardinal for which the consistency of having a universal order is known. As for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. As a result of the nonexistence of a universal linear order, we show the nonexistence of universal models for all theories possessing the strict order property (for example, ordered fields and groups, Boolean algebras, p-adic rings and fields, partial orders, models of PA and so on). (shrink)

PROBLEM: THE BEING OF NONEXISTENTS. In matters of irreality, medieval philosophers were not much concerned with fiction as such. The prime focus of their attention was theology, and their dealings with nonexistence related to the role of such items in relation to the thoughts of God rather than those of man. In this light, the medievals approached the issue of nonexistents on essentially the following basis.

This essay argues for the importance of developing theories of nonexistent objects. The grounds are utility and smoothness of logical theory. In the latter case a parallel with the theory of negative and imaginary numbers is exploited. The essay concludes with a counterexample to a general argument against the enterprise of developing theories of nonexistent objects, and outlining the foremost problem an adequate theory of nonexistent objects must solve.

Reconsideration-proofness is a solution concept proposed by Kocherlakota :33–54, 1996) for infinite horizon single-player problems in which time inconsistency is important. Kocherlakota’s definition has a limitation: it is not applicable to environments with state variables. The limitation is important because many time-inconsistent problems have state variables. This paper displays a natural generalization of reconsideration-proofness to environments with state variables, and shows that it leads to nonexistence in three examples. Such nonexistence contrasts with the general existence theorem obtained in (...) environments without state variables in Kocherlakota. In the first two examples, existence can be recovered with a modification in the solution concept. In the last example, nonexistence occurs even with the modified solution concept. Insights about further research are derived from these nonexistence results. (shrink)

Some believe that the harm or benefit of existence is assessed by comparing a person's actual state of wellbeing with the level of wellbeing they would have had had they never existed. This approach relies on ascribing a state or level of wellbeing to ‘nonexistent people’, which seems a peculiar practice: how can we attribute wellbeing to a ‘nonexistent person'? To explain away this oddity, some have argued that because no properties of wellbeing can be attributed to ‘nonexistent people’ such (...) people may be ascribed a neutral or zero level of wellbeing, setting the baseline for comparatively assessing the harm or benefit of coming into existence. However, this line of argumentation conflates the category of having zero wellbeing with the category of having no wellbeing. No Φ, unlike a zero level of Φ, is not comparable to levels of Φ — neutral, positive, or negative. Considering the nature of wellbeing and the fact that ‘nonexistent people’ cannot (metaphysically or conceptually) have wellbeing determinative properties, it follows that ‘nonexistent people’ have no wellbeing rather than zero wellbeing. (shrink)

Alexius Meinong claimed to uncover a brave new world of nonexistent objects. He contended that unreal objects, such as the golden mountain and the round square, genuinely had properties and therefore, deserved a place in an all-inclusive science. Meinong’s notion of nonexistents was initially not well-received, largely due to the influence and criticisms of Bertrand Russell. However, it has gained considerable popularity in more recent years as academics have uncovered shortfalls in Russell’s philosophy and strived to explain apparent “facts” about (...) the beingless. Some philosophers have continued Meinong’s project, further explaining nonexistent objects or formulating logic systems that incorporate them. The more recent developments beg for a re-examination of Meinongianism. This book does just that, putting the theory on trial. Part One considers if Russell truly defeated Meinongianism. It addresses Meinongian rejoinders in response to Russell’s main criticisms and further defends Russell’s alternative solution, his Theory of Descriptions. Part Two explores the rationale for nonexistents and their use in interpreting three types of statements: characterization, negative existential, and intentional. The book argues that, despite appearances, Meinongianism cannot plausibly account for its own paradigm claims, whereas Russell’s framework, with some further elucidation, can explain these statements quite well. Part Three primarily addresses claims about fiction, exploring the short-comings of Meinongian and Russellian frameworks in interpreting them. The book introduces a contextualization solution and symbolic method for capturing the logical form of such claims – one with the complexity to handle cross-contextual statements, including negative existential and intentional ones. It finally considers where that leaves nonexistent objects, ultimately rejecting such so-called entities. (shrink)

Fiction, Reference, and Nonexistence contains a new, contemporary theory of fiction and discusses the connection between language and reality. Martinich and Stroll, two of America's leading philosophers, explore fiction and undertake an analytic philosophical study of fiction and its reference, and its relation to truth.

Platonism considers existence as well as nonexistence as genuine properties. Kant and others have denied the former and the latter seems absurd. I reply that critics have forgotten that Platonism means accepting properties that are neither exemplified (like being a unicorn) nor exemplifiable (like nonexistence). I also present a Platonist analysis of negative existentials without appealing to nonexistence.

Tim Crane's The Objects of Thought is, I think, a much needed corrective to standard ways that analytic philosophers think about nonexistence. It starts from our common sense thought and talk, and tries to carve out a position that can defend this starting point in the face of criticism. It is well-written, a pleasure to read, and largely clear. I would recommend it to anyone interested in the problems of nonexistence. In §1 I sketch Crane's central ideas about (...) the nonexistent, before turning to themes that I would like to have heard more about. In §2, I distinguish two problems of nonexistence, showing that whilst Crane solves one, he does not address the other. Although Crane did not seek to address both problems, I think we should recognize that there is this residual problem of nonexistence remaining. Next (§3), I argue that whilst Crane is correct to think that a negative free logic has to be rejected if we construe it as making a claim about grammatical subject-predicate sentences, we might be able to salvage it if we recognise a class of logical predicates. But whether this is possible or not, depends on the solution to the unaddressed problem of nonexistence. In the final two sections I briefly raise a concern about Crane's view of quantification, before making a suggestion about his view might be employed in addressing Geach's problem of intentional identity. (shrink)

PREFACE Alexius Meinong (1853–1920) wrote an array of books and articles, broad in subject matter and rich in ideas. My book does not pretend to uncover the ...

This paper explores a new non-deflationary approach to the puzzle of nonexistence and its cousins. On this approach, we can, under a plausible assumption, express true de re propositions about certain objects that don’t exist, exist indeterminately or exist merely possibly. The defense involves two steps: First, to argue that if we can actually designate what individuates a nonexistent target object with respect to possible worlds in which that object does exist, then we can express a de re proposition (...) about “it”. Second, to adapt the concept of outer truth with respect to a possible world – a concept familiar from actualist modal semantics – for use in representing the actual world. (shrink)

Brentano's famous thesis of the Intentionality of the Mental was already formulated by Thomas Reid who used it in his campaign against the Locke-Berkeley-Hume Theory of Ideas. Apphed to the case of conceiving the thesis says that to conceive is to conceive something. This principle stands in apparent conflict with the common-sensical view, defended by Reid, that we can conceive what does not exist. Both principles, it is argued, are plausible and should be retained. The problem is how to resolve (...) the apparent contradiction. Reid's way out of the dilemma is clarified by contrasting it with less satisfactory solutions. (shrink)

A generic computation of a subset $A$ of $\mathbb{N}$ consists of a computation that correctly computes most of the bits of $A$, and never incorrectly computes any bits of $A$, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic (...) computability, answering a question of Jockusch and Schupp. (shrink)

An electron clearly has the property of having a charge of þ1.6 10 19 coulombs, but does it also have the property of being charged ? Philosophers have worried whether so-called ‘determinable’ predicates, such as ‘is charged’, actually refer to determinable properties in the way they are happy to say that determinate predicates, such as ‘has a charge of þ1.6 10 19 coulombs’, refer to determinate properties. The distinction between determinates and determinables is itself fairly new, dating only to its (...) definition by the Cambridge logician W. E. Johnson early in the last century.1 But despite its newly minted condition the distinction has found little currency in on-going philosophical debates. Or at least until recently. Renewed interest in realist positions about properties, and arguments that the determinable-determinate relation may hold the key to understanding mental causation, have thrust Johnson’s distinction to the fore. With this new attention has also come new ‘optimistic’ positions that endorse the existence of determinable properties. David Armstrong, Evan Fales, and Sydney Shoemaker, among others, have all defended such optimistic accounts that take determinable predicates, such as ‘is charged’, to refer to determinable properties.2 In this paper, our goal is to carefully assess optimism and to argue that a pessimistic view, which rejects the existence of determinable properties, is actually the appropriate default position. (shrink)

How is it that, as fiction readers, we are nonplussed by J. K. Rowling's prescription to imagine Ronan, Bane, and Magorian, three different centaurs of the Forbidden Forrest at Hogwarts? It is usually held in the philosophical literature on fictional discourse that singular imaginings of fictional objects are impossible, given the blatant nonexistence of such objects. In this paper, I have a dual purpose: on the one hand, to show that, without being committed to Meinongeanism, we can explain the (...) phenomenon of singular imaginings of different nonexistents of the same kind; while, at the same time, to attribute this position to Thomas Reid, thus correcting some misunderstandings of his view on imagination. (shrink)

IN THIS study I shall concentrate on three leading philosophical and theological thinkers of the thirteenth century: Thomas Aquinas, Henry of Ghent, and Godfrey of Fontaines. Of these, Thomas Aquinas is surely the best known. But I have selected these three because their discussions of nonexisting possibles are sufficiently different from one another to illustrate some of the major solutions proposed to this issue at that time.

This is the second of three papers on issues of personal identity, existence, and nonexistence. Here I argue that the birth of a child leads us to before and after value judgments that appear to be inconsistent. Consider, for example, a 14-year-old girl who decides to have a baby. We tend to think that the birth of a child to a 14-year-old would be a very unfortunate event, and hence that she should not decide to have a child. But (...) once the child has been born, we are loath to say that it shouldn't have been born. This conundrum is one of several that Derek Parfit considers in Part IV of Reasons and Persons. I suggest a solution that Parfit doesn't consider. Parfit's discussion is predicated on the assumption that our value judgments must be consistent, in the sense that they could be satisfied by some possible distribution of value across the possibilities. As we would say in logic, there must be a model of our value judgments, consisting in a distribution of value. I think that the present case gives us reason to reject this assumption. (shrink)

This is a forthright and refreshing book. It aims to bring the clarifying power of analytic philosophy to the luxuriant variety in one part of Meinong's ontology. Parson's title is meant to be read literally: it is not propositions, numbers, universals or sets, but only particular objects whose nonexistence concerns him. Parsons gives two reasons for believing that there are nonexistent objects. First, we match objects against the sets of their properties. When every existing object has been listed, we (...) carry on making sets of properties. These additional sets correlate with nonexistent objects, e.g., the golden mountain. Second, there are the many occasions when we use names or definite descriptions to characterize truly such nonexistent objects as Pegasus and Sherlock Holmes. There is, says Parsons, no satisfactory reason for rephrasing these sentences when we refuse to paraphrase sentences of the same form having existing objects as their referents. (shrink)

Holmes exists is false. How can this be, when there is no one for the sentence to misdescribe? Part of the answer is that a sentence’s topic depends on context. The king of France is bald, normally unevaluable, is false qua description of the bald people. Likewise Holmes exists is false qua description of the things that exist; it misdescribes those things as having Holmes among them. This does not explain, though, how Holmes does not exist differs in cognitive content (...) from, say, Vulcan does not exist. Our answer builds on an observation of Kripke’s: even if Holmes exists, he is not in this room, for we were all born too late. (shrink)

We prove that there are no binary homogeneous pseudoplanes.

Given two unital C*-algebrasA, ℬ and their state spacesE A , Eℬ respectively, (A,E A ) is said to have (ℬ, Eℬ) as a hidden theory via a linear, positive, unit-preserving map L: ℬ →A if, for all ϕ εE A , L*ϕ can be decomposed in Eℬ into states with pointwise strictly less dispersion than that of ϕ. Conditions onA and L are found that exclude (A,E A ) from having a hidden theory via L. It is shown in (...) particular that, ifA is simple, then no (ℬ, Eℬ) can be a hidden theory of (A,E A ) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra ℬ such that (ℬ, Eℬ) is a hidden theory of (A,E A ) via a conditional expectation from ℬ ontoA. (shrink)

The dead are gone. They count for nothing. Yet, if we count the dead, their number is staggering. And they account for most of what is great about civilization. Compared to the greatness of the dead, the accomplishments of the living are paltry. Which is it then: are the dead still there tobe counted or not? And if they are still there, where exactly is "there"? We are confronted with the ancient paradox of nonexistence bequeathed us by Parmenides. The (...) mystery of death is the mystery of nonexistence.A successful attempt to provide a metaphysics of death, then, must resolve the paradox of nonexistence. That is the aim of this study. At the same time, the metaphysics of death, of ceasing to exist, must serve as an account of birth, of coming to exist; the primary thesis of this book is that thisdemands going beyond existence and nonexistence to include what underlies both, which one can call, following tradition, "being." The dead and the unborn are therefore objects that lack existence but not being. Nonexistent objects - not corpses, or skeletons, or memories, all of which are existentobjects - are what are "there" to be counted when we count the dead. (shrink)

Suppose that by the term God we mean, among other things, a being who has always been in existence. Although this may not be what all theologians or philosophers who use that term would claim, it does not seem to be unreasonable to make the claim. The only alternative would be to claim, not of course that God began to exist at a certain time, but that he does not exist in time. But since such a claim seems to be (...) difficult to give a meaning, I prefer the more reasonable claim, to common sense at least, that God must be a being who always has been in existence. But despite the fact that the claim of always having been in existence appears to be a meaningful claim, it nevertheless is a concept which easily collapses. (shrink)

Fiction, Reference, and Nonexistence contains a new, contemporary theory of fiction and discusses the connection between language and reality. Martinich and Stroll, two of America's leading philosophers, explore fiction and undertake an analytic philosophical study of fiction and its reference, and its relation to truth.

Nonexistence is ubiquitous, yet mysterious. This volume explores some of the most puzzling questions about non-being and nonexistence, from metaphysics to ethics and beyond: the contributors offer answers from diverse philosophical perspectives, drawing on analytic, continental, Buddhist, and Jewish philosophical traditions.

The authors develop an axiomatic theory of nonexistent objects and and give a formal semantics for the language of the theory.